A model combining acid-mediated tumour invasion and nutrient dynamics

摘要

We illustrate a mathematical model for the evolution of multicellular tumour spheroids in a host tissue, including the effect of the excess H+ ions and the nutrient dynamics. Both the avascular and the vascular case are considered. The model is a nontrivial generalization of the simple scheme proposed in [K. Smallbone, D.J. Gavaghan, R.A. Gatenby, P.K. Maini, The role of acidity in solid tumour growth and invasion, J. Theoret. Biol. 235 (2005) 476-484]. Many different situations may occur, depending on the values of the physical parameters involved. Existence of solutions and qualitative properties are investigated.